The overall formation constant of the following reaction is `1 xx 10^(19)`
`Co^(+2) +6CN^(-) Leftrightarrow [Co(CN)_(6)]^(-3)`
Calculate formation constant of following comples
`Co^(+3) +6CN^(-) Leftrightarrow[Co(CN)_(6)]^(-3)`
Given that `[Co(CN)_(6)]^(-4) to [Co(CN)_(6)]^(-3) +e^(-), E^(0)=-0.83V`
`Co^(+3) +e^(-) to Co^(+2), E^(0)=1.82 V`

Explanation

`CO^(+2) +6CN^(-) Leftrightarrow [Co(CN)_(6)]^(-4)`
`K_(1)=([Co(CN)_(6)]^(-4))/([Co^(+2)][CN^(-)]^(6))`
And `Co^(+#) +6CN^(-) Leftrightarrow [Co(CN)_(6)]^(-3)`
`K_(2)=([Co(CN)_(6)]^(-3))/([Co^(+3)] [CN^(-6)]^(6))`
`K_(2)/K_(1) =([Co(CN)_(6)]^(-3) [Co^(+2)])/([Co(CN)_(6)]^(-4) [Co^(+3)])`
`[Co(CN)_(6)]^(-4) to [Co(CN)_(6)]^(-3)+e^(-)" "E^(@)=-0.83V`
`Co^(+3)+e^(-) to Co^(+2) " "E^(@)=1.82V`
Net cell reaction `Co^(+3) +[Co(CN)_(6)]^(-4) to Co^(+2) +[Co(CN)_(6)]^(-3)" "E_("Cell")^(@)=0.99V` at equilibrium `E_("cell")=0`
`E_("cell")^(@)=(0.0591)/(n) log K_(eq)`
`0.99=(0.0591)/(1) log ([Co^(2+)] [Co(CN)_(6)]^(-3))/([Co^(+3)] [Co(CN)_(6)]^(-4))=(0.059)/(1) log ""K_(2)/K_(1)`
`K_(2)/K_(1)=5.64 xx 10^(16)=K_(2)/10^(19) =8.23 xx 10^(44)`
`K_(2)=8.23 xx 10^(63)`